Some Properties on the Error-Sum Function of Alternating Sylvester Series

DOI: 10.4236/apm.2012.26070   PDF   HTML   XML   3,836 Downloads   5,889 Views  

Abstract

The error-sum function of alternating Sylvester series is introduced. Some elementary properties of this function are studied. Also, the hausdorff dimension of the graph of such function is determined.

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H. Jing and L. Shen, "Some Properties on the Error-Sum Function of Alternating Sylvester Series," Advances in Pure Mathematics, Vol. 2 No. 6, 2012, pp. 459-463. doi: 10.4236/apm.2012.26070.

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1] S. Kalpazidou, A. Knopfmacher and J. Knopfmacher, “Lüroth-Type Alternating Series Representations for Real Numbers,” Acta Arithmetica, Vol. 55, No. 4, 1990, pp. 311-322.
[2] K. H. Indiekofer, A. Knopfmacher and J. Knopfmacher, “Alternating Balkema-Oppenheim Expansions of Real Numbers,” Bulletin de la Société Mathématique, Vol. B44, 1992, pp. 17-28.
[3] S. Kalpazidou, A. Knopfmacher and J. Knopfmacher, “Metric Properties of Alternating Lüroth Series,” Potugaliae Mathematica, Vol. 48, No. 3, 1991, pp. 319-325.
[4] J. Barrionuevo, M. Burton-Robert, Dajani-Karma and C. Kraaikamp, “Ergodic Properties of Generalized Lüroth Series,” Acta Arithmetica, Vol. 74, No. 4, 1996, pp. 311-327.
[5] K. Dajani and C. Kraaikamp, “On Approximation by Lüroth Series,” Journal de Théorie des Nombres de Bordeaux, Vol. 8, No. 2, 1996, pp. 331-346. doi:10.5802/jtnb.172
[6] K. J. Falconer, “Fractal Geometry, Mathematical Foundations and Applications,” Wiley, Hoboken, 1990.
[7] K. J. Falconer, “Techniques in Fractal Geometry,” Wiley, Hoboken, 1997.
[8] J. Galambos, “Reprentations of Real Numbers by Infinite Series,” Lecture Notes in Math, Springer, Berlin, 1976.
[9] L. M. Shen and J. Wu, “On the Error-Sum Function of Lüroth Series,” Mathematics Analysis and Applications, Vol. 329, No. 2, 2007, pp. 1440-1445.
[10] L. M. Shen, C. Ma and J. H. Zhang, “On the Error-Sum Function of Alternating Lüroth Series,” Analysis in Theory and Applications, Vol. 22, No. 3, 2006, pp. 223-232. doi:10.1007/s10496-006-0223-x
[11] T. Sálat and S. Znám, “On the Sums of Prime Powers,” Acta Universitatis Palackianae Olomucensis of Mathematica, Vol. 21, 1968, pp. 21-25.

  
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